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A357259
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a(n) is the number of 2 X 2 Euclid-reduced matrices having determinant n.
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1
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1, 2, 3, 5, 5, 8, 7, 11, 10, 14, 11, 19, 13, 20, 18, 24, 17, 30, 19, 31, 26, 32, 23, 44, 26, 38, 34, 45, 29, 54, 31, 52, 42, 50, 38, 70, 37, 56, 50, 70, 41, 76, 43, 73, 63, 68, 47, 97, 50, 80, 66, 87, 53, 100, 62, 96, 74, 86, 59, 132, 61, 92, 85, 109, 74, 124, 67, 115, 90, 118
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OFFSET
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1,2
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COMMENTS
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See Bacher link for the definition of Euclid-reduced.
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LINKS
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FORMULA
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a(n) = Sum_{d|n, d^2>=n} d+1-n/d.
a(n) = Sum_{d|n} max(d-n/d, 1).
a(n) = ceiling(tau(n)/2) + (1/2)*Sum_{d|n} abs(d-n/d).
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MAPLE
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with(numtheory): seq(add(max(d-n/d, 1), d in divisors(n)), n=1..80); # Ridouane Oudra, Oct 30 2023
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MATHEMATICA
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a[n_] := DivisorSum[n, # + 1 - n/# &, #^2 >= n &]; Array[a, 100] (* Amiram Eldar, Sep 21 2022 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, if (d^2 >= n, d+1-n/d));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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